Statistical Models | Open Access Articles | Digital Commons Network™

Inversion Copulas From Nonlinear State Space Models With An Application To Inflation Forecasting, Michael S. Smith, Worapree Ole Maneesoonthorn

Michael Stanley Smith

We propose the construction of copulas through the inversion of nonlinear state space models. These copulas allow for new time series models that have the same serial dependence structure as a state space model, but with an arbitrary marginal distribution, and flexible density forecasts. We examine the time series properties of the copulas, outline serial dependence measures, and estimate the models using likelihood-based methods. Copulas constructed from three example state space models are considered: a stochastic volatility model with an unobserved component, a Markov switching autoregression, and a Gaussian linear unobserved component model. We show that all three inversion copulas …

Go to article

Implicit Copulas From Bayesian Regularized Regression Smoothers, Nadja Klein, Michael S. Smith

Michael Stanley Smith

We show how to extract the implicit copula of a response vector from a Bayesian regularized regression smoother with Gaussian disturbances. The copula can be used to compare smoothers that employ different shrinkage priors and function bases. We illustrate with three popular choices of shrinkage priors --- a pairwise prior, the horseshoe prior and a g prior augmented with a point mass as employed for Bayesian variable selection --- and both univariate and multivariate function bases. The implicit copulas are high-dimensional and unavailable in closed form. However, we show how to evaluate them by first constructing a Gaussian copula conditional on the regularization parameters, …

Go to article

From Amazon To Apple: Modeling Online Retail Sales, Purchase Incidence And Visit Behavior, Anastasios Panagiotelis, Michael S. Smith, Peter Danaher

Michael Stanley Smith

In this study we propose a multivariate stochastic model for website visit duration, page views, purchase incidence and the sale amount for online retailers. The model is constructed by composition from carefully selected distributions, and involves copula components. It allows for the strong nonlinear relationships between the sales and visit variables to be explored in detail, and can be used to construct sales predictions. The model is readily estimated using maximum likelihood, making it an attractive choice in practice given the large sample sizes that are commonplace in online retail studies. We examine a number of top-ranked U.S. online retailers, …

Go to article

Statistical Models Commons^™

Full-Text Articles in Statistical Models

Inversion Copulas From Nonlinear State Space Models With An Application To Inflation Forecasting, Michael S. Smith, Worapree Ole Maneesoonthorn

Michael Stanley Smith

Implicit Copulas From Bayesian Regularized Regression Smoothers, Nadja Klein, Michael S. Smith

Michael Stanley Smith

From Amazon To Apple: Modeling Online Retail Sales, Purchase Incidence And Visit Behavior, Anastasios Panagiotelis, Michael S. Smith, Peter Danaher

Michael Stanley Smith